1 Model-Driven Engineering of Gene Expression from RNA Replicons2 Jacob Beal,*,†,† Tyler E. Wagner,‡,† Tasuku Kitada,§ Odisse Azizgolshani,∥ Jordan Moberg Parker,⊥

3 Douglas Densmore,‡ and Ron Weiss§

4†Raytheon BBN Technologies, Cambridge, Massachusetts United States

5‡Center of Synthetic Biology, Boston University, Boston, Massachusetts 02215, United States

6§Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States

7∥Department of Chemistry and Biochemistry, University of California Los Angeles, Los Angeles, California 90095-1570, United States

8⊥Department of Microbiology, Immunology and Molecular Genetics, University of California Los Angeles, 609 Young Drive, Box

9 148906, Los Angeles, California 90095-1570, United States

10 *S Supporting Information

11 ABSTRACT: RNA replicons are an emerging platform for engineering12 synthetic biological systems. Replicons self-amplify, can provide persistent13 high-level expression of proteins even from a small initial dose, and, unlike14 DNA vectors, pose minimal risk of chromosomal integration. However, no15 quantitative model sufficient for engineering levels of protein expression from16 such replicon systems currently exists. Here, we aim to enable the engineering17 of multigene expression from more than one species of replicon by creating a18 computational model based on our experimental observations of the19 expression dynamics in single- and multireplicon systems. To this end, we20 studied fluorescent protein expression in baby hamster kidney (BHK-21) cells21 using a replicon derived from Sindbis virus (SINV). We characterized22 expression dynamics for this platform based on the dose−response of a single23 species of replicon over 50 h and on a titration of two cotransfected replicons24 expressing different fluorescent proteins. From this data, we derive a quantitative model of multireplicon expression and validate25 it by designing a variety of three-replicon systems, with profiles that match desired expression levels. We achieved a mean error of26 1.7-fold on a 1000-fold range, thus demonstrating how our model can be applied to precisely control expression levels of each27 Sindbis replicon species in a system.28 KEYWORDS: quantitative modeling, circuit prediction, replicon, alphavirus, Sindbis, TASBE characterization, expression control,29 flow cytometry

30 Recently, interest has been growing in RNA replicons as31 standalone gene delivery vehicles.1 Two of the primary32 advantages of replicon-based systems are self-amplification33 and safety, making replicons an attractive modality for medical34 applications such as vaccine delivery, gene therapy, and cellular35 reprogramming.2−4 Because they are self-amplifying, replicons36 can generate high expression of a gene product, such as an37 antigen, from a relatively low initial dose, compared to38 nonreplicating RNA.5,6 The self-amplifying feature of replicons39 is particularly valuable for mammalian systems, in which40 replicating DNA-based vectors are uncommon and difficult to41 construct due to their complexity.7 Moreover, with regard to42 safety, replicons do not reverse transcribe and are confined to43 the cytoplasm of the cell, so the risk of undesired integration44 into the genome is minimal.8,9

45 Of the various replicons that have been developed, we have46 chosen to focus on a replicon derived from a Sindbis virus47 (SINV), the most well-characterized alphavirus.5 Sindbis48 replicons with reduced cytopathicity and increased duration49 of expression have been developed.10−14 SINV is a positive-50 strand RNA virus with an 11.7 kilobase genome. The SINV

51genome has a 5′-7-methylguanosine cap and a 3′-poly(A) tail,52both of which are characteristics of cellular mRNA, allowing53SINV to utilize existing cellular machinery to initiate translation54of its nonstructural proteins.15 The 5′ two-thirds of the SINV55genome encodes the four nonstructural proteins that act56together to form a replicase complex. Replication occurs57through a minus-strand intermediate template, which is used58for the synthesis of both the full length positive strand genome,59as well as the subgenomic RNA that comprises the 3′ one-third60of the genome.15−18 In the wild type virus, the subgenomic61RNA is the source of the structural proteins that allow the virus62to propagate to other cells. These structural proteins can be63replaced with an engineered sequence to produce alternate64 f1gene products, creating a replicon (Figure 1a): a general RNA65delivery vehicle that amplifies by self-replication, expresses

Special Issue: Summer Synthetic Biology Conference 2014

Received: March 7, 2014

Research Article

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66 specified gene products, and lacks the necessary structural67 proteins that would allow it to infect other cells.19−21

68 Initial work using replicon systems has focused mainly on69 producing a single protein product.15 Many applications,70 however, may require more sophisticated replicon-based71 circuits with multiple gene products at various different72 expression levels; these products may also need to be separately73 regulated or to regulate one another. A number of approaches74 to express multiple genes from replicons have been75 investigated, including the use of multiple subgenomic76 promoters,22−25 insertion of internal ribosome entry sites77 (IRES),25−27 and use of 2A sequences.28−30 Such approaches,78 however, have a number of limitations, including decreased or79 uneven expression, RNA recombination, and inherent scaling80 limits on the size of an effective replicon.31−33 Moreover, many81 RNA regulatory mechanisms, such as RNAi or those involving82 cellular nuclease complexes, operate via RNA degradation and83 thus will act on the replicon as a whole, thereby preventing the84 use of these mechanisms in single replicon systems to control85 individual gene products.34

86 In this manuscript, we adopt an alternate approach based on87 cotransfection of multiple replicons. With this approach, the88 coding sequences of a system are distributed onto more than89 one species of replicon, and the system is installed by mixing90 these species together in an appropriate titration and91 cotransfecting. This approach overcomes issues of replicon92 size and allows each replicon species to be titrated and93 regulated independently. Similar to multiplasmid systems,94 however, it introduces variability into the stoichiometry of the95 system, including the possibility that a cell may receive only96 part of the system. Precise regulation of a gene product from a

97single replicon may also benefit from this approach: as we show98in this manuscript, single replicon systems tend to saturate to99the same final expression level, independent of initial dose,100which poses a problem when engineering expression of a single101protein product. Using the cotransfection model that we102develop in this manuscript, however, the expression of a desired103protein can be tuned using a second “ballast replicon” that104competes for expression resources.105Thus, we develop cotransfection as a method to enable the106precision engineering of protein expression from replicons by107constructing a predictive quantitative model of replicon108expression dynamics. To this end, we measure the dose−109response behavior of a single species of Sindbis replicon in110BHK-21 cells over time, and of varying titrations of two111cotransfected replicon species. From this data, we derive a112quantitative model of multireplicon expression, which we then113validate by applying it to design a collection of six three-114replicon systems with a range of expression profiles. The115experimental behavior of these systems matches our desired116expression levels to a mean accuracy of 1.7-fold on a 1000-fold117range, thus demonstrating the capability of our model to118precisely control gene expression of each Sindbis replicon in a119system.

120■ RESULTS121The design of the Sindbis replicons we used and the main122processes involved in expression from such replicons are shown123in Figure 1. First, the transfection process introduces some124number of “founder” replicons into each cell. Using the native125translational machinery, these replicons begin to express126proteins, specifically a set of nonstructural proteins used for

Figure 1. (a) We investigated replicon dynamics using Sindbis replicons with reduced cytopathicity10 containing the nsP2 P726S mutation (top), inwhich the portion of the RNA sequence coding for the SINV structural proteins is replaced by an engineered “payload” sequence, such as afluorescent protein. (b) In replicon-based expression, initially a set of “founder” replicons enter the cell during transfection. The nonstructuralproteins (nsPs) expressed from the replicons create “viral factories” in which the number of replicons is amplified exponentially. This process alsoproduces subgenomic transcripts containing the “payload” sequence, which are expressed into proteins. Expression levels may be limited by theordinary processes of degradation and dilution, as well as resource limits, antiviral innate immune response, and gross cell effects such as apoptosis,necrosis, and blebbing.

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127 replication. These proteins, through processes not yet fully128 understood, modify endosomes and lysosomes to create “viral129 factories” in which they replicate the RNA.35,36 The replication130 process also produces transcripts of the 3′ subgenomic131 sequence or sequences encoding an engineered “payload,”132 which are translated to express the encoded proteins. These133 proteins are then degraded by typical cellular mechanisms.134 Protein expression may be inhibited by type-I interferon (IFN)135 mediated cellular antiviral innate immune responses,37 or by136 gross cellular events such as apoptosis, necrosis, and blebbing.137 Here, we use BHK-21 cells (an IFN deficient cell line) as the138 host cell for Sindbis replicon expression to reduce possible139 complications that the innate immune response may have on140 gene expression. Expression is also self-regulated by the141 nonstructural protein complex, which self-cleaves and alters142 the polarity of the RNA-dependent RNA replication complex.15

143 This mechanistic model implies a set of hypotheses regarding144 the expression patterns that may be expected in a replicon145 system with a constitutively expressed stable reporter protein,146 such as mVenus, mKate, or EBFP2. First, as transfection is a147 stochastic chemical process, the fraction of cells transfected148 should be dose-dependent. Moreover, if the replicons are well-149 mixed and transfections proceed independently (a reasonable150 null hypothesis), the number of transfections per cell would be151 expected to follow a Poisson distribution. Possible behaviors

f2 152 range between two asymptotic phases (Figure 2a): a “sparse”153 phase for lower doses, in which a small fraction of cells are

154successfully transfected with a single founder replicon and155fluoresce, and “dense” phase for higher doses, in which nearly156all cells receive many founder replicons and fluoresce.157Multireplicon systems will generally need to operate in the158“dense” phase such that the probability distributions can be159engineered to provide a high likelihood of all replicon species160being delivered to each cell with good control of their161stoichiometry.162For those cells that are transfected and fluoresce, the163progress of fluorescent protein expression over time will be164determined by the relative amount of available resources for165replication and translation, or by alternative mechanisms for the166reduction of expression, including antiviral innate immune167responses or the degradation of RNA (Figure 2b). Replication168is expected to initially be exponential, but the number of169replicon copies must eventually saturate as either available170resources become depleted or the replication process becomes171inhibited by itself or the cellular host. At low replicon densities,172translation is expected to be linear in the number of copies of173the replicon, meaning that during the initial exponential174replication phase, fluorescence will rise exponentially, tracking175the rise in replicon copies with some delay. If translational176resources become depleted or the translation process becomes177inhibited, then fluorescence will rapidly converge to a stable178expression level. If such a limit is not reached, on the other179hand, then fluorescence will continue to increase until protein180translation is balanced by dilution and/or decaya long period181of at least several cell divisions or protein half-lives.182Single Replicon Transfection. To determine which of183these hypotheses best describes the expression dynamics of184Sindbis replicons in BHK-21 cells, we measured the dose−185response behavior of cells over the course of 50 h post-186 f3transfection (Figure 3a). We transfected BHK-21 cells with187Sindbis replicon containing a gene for a fluorescent reporter,188mVenus, at logarithmic doses (21, 41, 103, 206, 411, 1027,1892055 ng per 1 × 105 cells). Fluorescence was measured using190flow cytometry at 1, 3, 5, 7, 9, 11, 16, 19, 21, 26, 35, and 50 h191post-transfection. We found that the transfected population of192cells exhibits behavior consistent with being translation-limited,193with an extremely sharp rise in mean fluorescence that rapidly194saturates. Alternatively, if fluorescent expression were primarily195replication-limited, the rate of convergence to saturation would196be dominated by the process of achieving equilibrium between197production and loss of protein, which should have a time198constant on the order of the division time of the cells. Instead,199we observe a much faster convergence consistent with200translational resource depletion having at least a similar level201of importance to replication rates: all dosages converged to a202consistent expression level by 16 h and remained relatively203stable thereafter (Figure 3a). Before that point, however, there204is a monotonic relationship between dose and expression205(Figure 3b), suggesting that, at lower dosages, limits on206replication are also affecting the course of expression. With this207data, we constructed an approximate model of mean protein208expression using the following formula derived from the209hypothesis that protein expression is strongly regulated by210translational resources:

= − δ λ−E t S( ) max(0, (1 2 ))t/E E

211where E(t) is the expression at time t, S is the saturated212expression level, δE is an initial delay representing the early213phase of the exponential replication process, and λE is the time214constant on the exponential convergence toward saturation.

Figure 2. Depending on the relative dose and resources, a repliconsystem is expected to exhibit qualitatively different phases of behavior.(a) With a very low RNA dose (left), we expect to see only a few cellssuccessfully transfected, and each transfected cell to receive only asingle “founder” replicon. At the opposite extreme (right), high dosesare expected to put many founder replicons into every cell, inproportion to their fraction of the initial dose. At intermediate levels,most cells will be transfected, but the relative stoichiometry of founderreplicons will vary widely. (b) The translation and replicationprocesses are both limited in the amount that they can driveresources. If the replication limit is reached much earlier than thetranslation limit (left), then expression will rise almost linearly for along time before slowly reaching an equilibrium. In the oppositeextreme, where the translational limit is reached while replication isstill proceeding rapidly, then expression will rise exponentially to asharp limit (right). When both limits are approached at similar rates,expression will rise quickly and then decelerate to an equilibrium.Graphs are ODE simulations varying relative rate constants byapproximately 300×, plotted using linear axes.

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215 The delay before significant expression can be observed is due216 to the delivery and replication process; in principle, we should217 be able to model the dynamics of the development of viral218 factories and the dose-dependent rise of expression with respect219 to time. In this work, however, we restrict our model to the 1-220 DOF approximation of a fixed delay δE (rather than dose-221 dependent) because the signal from this process in our data is222 not sufficient to fit a more complex model within reasonable223 bounds (Supporting Information section 2), and (as will be224 seen) abstracting away dose-dependent delay is not the limiting225 factor on the precision of our predictions.226 Figure 3c compares this model (fit to parameters S = 1.05 ×227 108 MEFL, δE = 4.02 h, and λE = 5.86 h) against all of the time228 points gathered through 26 h. The model fits the data well, with229 the fit having a mean geometric error of 1.07-fold between230 model and prediction after 5 h, once detectable expression is231 expected to begin. Note, however, that although this model232 indicates that expression saturates due to a limit on the233 translation process, it does not disambiguate between other234 reasons that translation might decrease or cease, such as235 resource depletion, innate immune response, or cell death.236 The size of the fluorescently expressing population over time237 can also be predicted from time-course data. Figure 3d shows238 that the fraction of observably expressing cells versus time is239 strongly dose dependent. After the first three time points240 (covering the first 5 h, in which expression is still too low to241 observe well at most dosages), the fraction of fluorescent cells is242 stable at first but then begins to decrease. The pattern of

243decrease is consistent with a model in which replicons are244initially distributed into cells following a Poisson distribution245(per our mechanistic hypothesis above) and where cells that are246not transfected continue to divide, while those that are247transfected stop or drastically slow division once replicon and248expression levels are high. We thus model the fraction of249expressing cells:

τ α= >F d P d( , 0) (Pois( ) 0)

=+ − · δ λ−F d t F d

F d F d( , ) ( , 0)

( , 0) (1 ( , 0)) max(1, 2 )t/F F

250where F(d,t) is the fraction of cells expressing at time t given251initial dose d, τ is an ideal transfection efficiency (modeling the252fact that some cells may fail to be transfected regardless of253dose), P(Pois(αd) > 0) is the probability of a sample being254greater than zero when drawn from a Poisson distribution255parametrized by dose times a constant α, δF is the delay before256cell division is affected in transfected cells, and λF is the rate at257which untransfected cells out-divide transfected ones. Figure 3d258compares this model (fit to parameters τ = 0.977, α = 0.0127,259δF = 21.5 h, and λF = 8.89 h) against time points beginning at 9260h, showing that it is a good fit, with a mean error of 2.5%. Note261that although we have quantified the effect on division, it might262actually be caused by any number of mechanisms: candidates263include resource sequestration, toxicity from the action of the264replicon, innate immune response, or some mixture thereof.265This data also does not distinguish between failure to divide

Figure 3. (a) Evolution of fluorescent expression over time for logarithmically varied doses of replicon, showing for all doses a rapid rise toward aconsistent dose-independent level. Data shown is mean for upper (transfected) component of bimodal log-normal fit to fluorescence distribution.Dose is indicated by hue, ranging geometrically from 21 ng/μL (magenta) to 2055 ng/μL (yellow). (b) Detail of the first 11 h. (c) The rise towardsaturation over the first 26 h shows that observations are well fit by a resource limitation model. (d) The initial fraction of transfected cells is dose-dependent following a Poisson distribution, then decreases as transfected cells stop or drastically slow their rate of division. Expression units areMEFL: molecules of equivalent fluorescein.

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266 and slow division: our model only states how much faster the267 untransfected population is dividing than the transfected268 population.269 Another interesting implication of this model is that it270 appears that no replicon dosage can be low enough to cause271 this particular replicon/cell system to be primarily limited by272 replication. Given both the value of α that has been identified273 and the large number of nonexpressing cells at low dosage, we274 may reasonably hypothesize that many cells in the fluorescently275 expressing population are initially transfected with only a single276 replicon. In the 21 and 41 ng dose conditions, these cells are277 expected to make up the vast majority of the expressing278 population, and in the 103 ng dose condition are expected to be279 48% of the expressing population. Thus, further reduction of280 the initial dose may be expected to further decrease the fraction281 of expressing cells but will not result in any significant further282 shift toward expression being primarily limited by replication.283 Multi-replicon Transfection. In the discussion above, we284 established a model that estimates the fraction of cells with285 active replicons and the mean expression from a single species286 of replicon within these cells. For engineering systems based on287 multireplicon cotransfection, however, it will also be important288 to have a model of the degree of variation anticipated from cell289 to cell, since small variations in the founder population of290 replicons may lead to large differences in the relative291 populations following exponential replication. To quantify292 variation, we transfected BHK-21 cells with pairs of replicons293 that are identical except for the choice of fluorescent reporter:294 mVenus/mKate, mKate/EBFP2, or mVenus/EBFP2. Each295 sample was transfected with 1390 ng total RNA, at varying296 titrations of the two replicons ranging from 0% to 100% in297 steps of 10%. Fluorescence was measured via flow cytometry 20

f4 298 h post-transfection (Figure 4). Based on our prior models, we299 expected transfection to be dense, with many founder replicons300 per cell. By the law of large numbers, this means that the mean301 fluorescence per cell should be approximately linear with302 respect to the relative dose (though they may be somewhat303 distorted by variation) and when converted to equivalent304 MEFL units the sum of the two fluorescence intensities should305 be equal to a constant. These predictions are borne out by our306 observations (Figure 4). We also refine our estimate of S to307 5.44 × 107 MEFL using the means of dual transfections, as the

308geometric means of this collection of high-dose conditions309provide a more reliable estimate than the bimodal Gaussian fit310used for tracking small expressing populations in the prior311experiment.312When considering distribution of fluorescence, however,313variation is much greater than can be accounted for only by a314pure Poisson distribution. We note two additional sources of315variation that are known to have large effects in biological316systems. First, most cells (including the BHK-21 cells we are317using) vary significantly in their size and state; this is expected318to affect both the resources available for expression and the319amount of founder population of replicons introduced during320transfection. Observing that single-replicon experiments show a321log-normal distribution of fluorescence (Supporting Informa-322tion Figure 1), we model a cell variation factor V as a log-323normal distribution:

= σV 10N(0, )

324where N(0,σ) is a normal distribution with standard deviation325σ. We include this variation factor as a multiplier in the326distribution of founder replicons, reflecting the hypothesis that327larger cells are likely to take up proportionally more replicons:

α=f VdPois( )i i

328where f i is the number of founder replicons of the ith replicon,329di is the partial dose of the ith replicon, and α is the same330parametrization constant that we fit previously in modeling the331fraction of transfected cells.332The second major known source of variation is the333stochasticity of biochemical processes when there are only a334few molecules. In many cases, the number of founder copies of335each replicon expected in a given cell may be quite low, in336which case the first few replication events may have a large337impact on the ultimate ratio of the two cotransfected replicons.338This can be modeled mathematically as a Polya Urn process.38

339The Polya Urn process considers an urn that begins with k340balls, each of which has some color; for each of n iterations, a341ball is drawn, then replaced along with an extra ball of the same342color, increasing the number of balls in the urn. This model has343the property that when the number of balls is small, the ratios344can shift significantly, but as the process continues the ratios345drift less, ultimately converging to a value distributed by a β

Figure 4. Cotransfection of two replicons at varying titrations and a constant high total dose produces a linear relation between relative dose andfluorescence (a) and a constant total fluorescence (b), as predicted from single-replicon models. Expression units are MEFL: molecules of equivalentfluorescein.

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346 distribution parametrized on the initial set of balls. Applied to347 model our replicon systems, the colors are the replicon species,348 the initial balls are the founder copies, and the draw and349 replacement process is replication events, giving a model of

∑ ∑β= −< >

p p f f(1 ) ( , )ij i

j ij i

j

350 where pi is the proportion of the ith replicon following351 replication and β(x,y) is the beta distribution.352 Note that this model of replication via a Polya Urn process is353 unlikely to be strongly affected by how replicons are distributed354 in viral factories, the process by which viral factories are formed,355 or the process by which RNA escapes the viral factories.356 Independent factories, each replicating its own collection of357 replicons, may be viewed as members of a “meta-urn” that358 produces the same distribution of converged ratios, as long as it359 is the case that many replicons can fit in a factory. Likewise,360 independent factories may be translated in time without a361 significant effect, as long as the variance in the time to form a362 factory is not so long as to allow other factories to significantly363 affect the available transcriptional resources. From our results, it364 appears that neither of these cases holds strongly enough to365 prevent the Polya Urn model from being a reasonable366 approximation of observed behavior. This does not, however,367 constrain the system enough to shed any significant new light368 on the behavior of viral factories.369 Combining these factors, we enhance our earlier model of370 mean protein expression for single replicons to a model giving a371 distribution of expression for multiple replicon species:

= − δ λ−E t i Vp S( , ) max(0, (1 2 ))it/E E

372 with the expression E(t,i) of the ith replicon at time t varying373 from the mean according to the cell variation factor and the374 distribution of the replicons’ proportions implied by the initial375 dose. Fitting this model against the set of 90%/10% titrations

f5 376 (to maximize observed variation), we obtain σ = 0.365 (Figuref5 377 5).

378 Engineering Multi-replicon Systems. We validated our379 expression model, as well as demonstrated how it can be used380 to engineer precision control of expression levels, by designing381 and predicting expression for a set of six three-replicon

t1 382 mixtures. These six mixture conditions, shown in Table 1,

383were chosen to evaluate the performance of our expression384model on a variety of systems with dosage levels and dosage385ratios ranging across approximately 2 orders of magnitude.386BHK-21 cells were transfected with each replicon mixture at the387specified dosages and fluorescence was measured by flow388cytometry at 3, 6, 11, 20, 26, 34, and 50 h post-transfection. In389all cases, our expression model provides a highly precise390prediction of the observed value, with a mean prediction error391 f6of only 1.7-fold (Figure 6a). With respect to individual392mixtures, there is no significant difference in prediction quality393(Figure 6b). With respect to time, prediction errors are slightly394lower at around 24 h, when the greatest number of cells are395fluorescing most strongly, but show no significant pattern for396when predictions are better or worse (Supporting Information397Figure 2). Means versus time for each mixture are shown in398Figure 6c and Supporting Information Figure 3. Finally, the399expression model predicts well not only the mean but also the400distributions of fluorescence within each sample (Figure 6d and401Supporting Information Figures 4−10).

402■ DISCUSSION403The work presented in this manuscript enables the use of RNA404replicons as a predictable platform for synthetic biology. We405have demonstrated that Sindbis replicon in BHK-21 cells has a406highly systematic pattern of gene product expression over time.407Expression can be predicted with high precision from the initial408replicon dosage, using an 8-DOF model. This model was409derived from the basic mechanisms of transfection, replication,410and translation, and parametrized using experimental observa-411tion of single- and dual-replicon transfections. Our model412allows predictive engineering of a multireplicon system, as we413have demonstrated by designing and precisely predicting the414expression distributions of a collection of six mixtures of three415replicons across a wide range of dosages and ratios.416The same approach can be applied to precision control of the417expression from a single-replicon system, by titrating with a418competing “ballast” replicon (note that changing the initial419dosage of a single replicon does not change the per-cell420expression level after the first few hours, only the fraction of421cells successfully transfected). Although our work enables the422immediate engineering of a wide range of RNA replicon423expression systems, further investigation is necessary to support424a full range of replicon-based applications. At present, our425models only apply to constitutive expression from replicons of426uniform size, with similar sized products, under control of427identical subgenomic promoters. Replicons of different sizes428may replicate at different rates, which would change the429mapping from founder population to the distribution of430converged ratios. Similarly, different gene products may require431different resources, which may affect their share of the432translational limit, and differences in subgenomic promoters433are also expected to affect expression. Regulatory interactions

Figure 5. Experimental observations vs model of fluorescencedistribution for all 10%:90% ratios of two-replicon transfection, in allsix dosage/color combinations.

Table 1. Dosages for Three-Replicon Mixtures Used forValidation of Model-Driven Design

condition mVenus (ng) mKate (ng) EBFP2 (ng)

1 180 180 1802 540 540 5403 180 900 7204 360 360 10805 18 180 9006 720 36 36

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434 between replicons will also affect expression dynamics,435 particularly when the mechanism of regulation involves RNA436 degradation. Finally, the nonstructural proteins of the replicon437 are translated as well; these are not included in our model at438 present because their effect can be factored out for constitutive439 expression from uniform replicons. However, if these non-440 structural proteins have a significant effect on expression, they441 too may need to be included in a more general computational442 model. In many cases, extending models to cover such systems443 is also likely to require a more explicit model of replication than444 the current coarse abstraction. Although the parameters of the445 system that we studied precluded building a comprehensive446 quantitative model from fluorescence data, such a model should447 be able to be acquired either from other replicons with lower448 levels of protein expression or by studying RNA levels directly,449 for example, via qRT-PCR. Understanding the contributions of450 different mechanisms to the translation limit will also be451 important for future engineering work.452 A concern for certain applications is the fact that the BHK-21453 cells stopped or drastically slowed dividing in vitro, which454 indicates gross cell effects that may preclude the use of Sindbis455 replicons in many therapeutic applications. However, other456 combinations of replicons and cell lines may show less impact,

457and published reports of sustained in vivo replicon expression458are quite promising.39 Since other replicon/cell combinations459are generally expected to have the same underlying biochemical460processes (except for the immune mechanisms that BHK-21461lacks), we expect that the same general models will likely apply,462though they will have different parameter values.463In summary, the methods and approach that we have464presented here provide a solid foundation for developing a465general capability for precision engineering of biological466systems using RNA replicons. Beyond replicons, this work467also provides an example of systematic establishment of a468quantitative engineering method for a biological mechanism,469some principles of which may be able to be extended more470broadly to other biological systems, such as DNA-based471transcriptional and translational gene circuits. Our model472construction depends critically on the use of per-cell measure-473ments, which allow distinction between expressing and474nonexpressing subpopulations and expose systematic effects475that would otherwise not be directly observable. It also depends476on being able to translate all fluorescence measurements into477equivalent absolute units, which allows data from different478fluorescent proteins to be compared directly in the two-479replicon titration experiments. Finally, we abstract mechanisms

Figure 6. Our Sindbis/BHK expression model successfully predicts the evolution of expression distributions for six three-replicon mixtures across awide range of initial dosages: (a) mean predicted vs measured expression for each color for all time/mixture combinations measured (mKate is red,EBFP2 is blue, and mVenus is green); (b) geometric mean fold error vs fold expression range for each of the six mixtures. Standard deviation isacross replicates for range and across replicates and colors for error. (c, d) Examples of prediction detail: (c) predicted vs experimental evolution ofmean expression for Mixture 4 (360 ng mVenus, 360 ng mKate, 1080 ng EBFP2) for 50 h post-transfection; (d) predicted vs experimentaldistribution of fluorescence values for Mixture 4 at 50 h post-transfection. Full details of predictions are shown in Supporting Information Figure 2through 10. Expression units are MEFL: molecules of equivalent fluorescein.

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480 where necessary in order to ensure that all parameters used by481 our model are well-supported by experimental data. Applying482 such methods in other contexts may likewise assist in the more483 general development of improved biological engineering484 models and methods.

485 ■ METHODS486 Cloning/RNA Generation. All Sindbis constructs were487 created from pSINV-EYFP using standard molecular cloning488 techniques.40 The replicon itself originated from the TE12489 strain of Sindbis and was altered to contain the previously490 characterized, less cytopathic P726S mutation in nsP2.10,11 The491 plasmids were linearized using SacI prior to in vitro tran-492 scription using the mMESSAGE mMachine SP6 Kit (Life493 Technologies). The resulting RNA was purified using the494 RNeasy Mini Kit (Qiagen) and the concentration was495 measured using the NanoDrop 2000.496 Transfection. All Sindbis transfections were conducted in497 BHK-21 cells (a kind gift from Dr. James H. Strauss) cultured498 in EMEM (ATCC) supplemented with 10% FBS (PAA) at 37499 °C and 5% CO2. BHK-21 cells at approximately 70%500 confluence were electroporated using the Neon Transfection501 System (Life Technologies) following optimization, according502 to the manufacturers’ instructions. In general, for a single well503 of a 24-well plate (Corning), approximately 100 000 cells were504 electroporated with RNA ranging from 18 to 2055 ng.505 For the time-course experiment, samples were taken in506 duplicate. For the dual transfection experiment, one sample was507 taken for each titration, with the single replicon samples508 (100%/0% titration) shared between color pairings. For the509 three-replicon mixtures, samples were taken in duplicate. Note510 that the statistical strength of results is not significantly511 weakened by using smaller numbers of samples per condition,512 due to the fact that conclusions are drawn from the joint513 analysis of groups of samples across varying conditions.514 Flow Cytometry. Cells for each time point were washed515 with 1× PBS, trypsinized, and resuspended in 1× PBS. Flow516 cytometry was performed using the BD LSRFortessa Flow517 Cytometer System and FACSDiva software was used for initial518 data collection.519 Statistical Analysis and Modeling. Flow cytometry data520 was converted from arbitrary units to compensated MEFL521 (Molecules of Equivalent FLuorescein) using the TASBE522 characterization method.41 An affine compensation matrix is523 computed from single positive and blank controls. FITC524 measurements are calibrated to MEFL using SpheroTech RCP-525 30-5-A beads,42 and mappings from other channels to526 equivalent FITC are computed from cotransfection of high527 equal dose (>500 ng) of replicons identical except for the528 choice of fluorescent protein. For dual transfection data, we use529 the 50:50 condition for each pair; for mixture data we use the530 26-h time point for condition 2. For Figure 3, expression data is531 fit against a bimodal Gaussian on the log scale to distinguish the532 subpopulation of cells where the replicon is successfully533 transfected from the subpopulation where it is not. Unlike534 gating thresholds, a bimodal Gaussian model allows good535 estimation of relative population sizes even when subpopula-536 tions overlap in their distribution of expression. Mean of537 expressing population is then calculated as the mean of the538 upper component of a bimodal log-normal fit to the observed539 distribution, except for time points 35 and 50 of lowest dosage,540 where expressing population is too small for a good fit, and we541 instead select the distribution peak at highest MEFL. For all

542other figures, where mixture of replicons skews distributions543away from log-normal, means are computed as geometric mean544of all samples >104 MEFL. Histograms are generated by545segmenting MEFL data into logarithmic bins at 10 bins/decade,546with geometric mean and variance computed for those data547points in each bin. Model fits are performed using standard548least-squares curve fitting on a linear scale. The model of549expression rising to saturation is fit against all but the two550lowest dosages, which appear to be significantly affected by551replication dynamics. The model of fraction transfected is fit552against all but the lowest dosage, where expression was too low553in some cases for bimodal Gaussian fits to converge. All554parameter estimates are expressed to three significant figures for555consistency.

556■ ASSOCIATED CONTENT557*S Supporting Information558List of exceptions to replicate numbers, a discussion of choices559in modeling replication, replicon sequences, and full details of560all predictions. This material is available free of charge via the561Internet at http://pubs.acs.org.

562■ AUTHOR INFORMATION563Corresponding Author564*Email: jakebeal@bbn.com.565Author Contributions

†566J.B. and T.E.W. contributed equally to this work. J.B., T.E.W.,567and R.W. designed experiments. T.E.W. performed the568experiments; T.K. assisted with experiments and performed569preliminary experiments. J.B. developed and applied computa-570tional analysis methods, developed computational models, and571developed methods for prediction and design of expression.572J.B., T.E.W., R.W., and T.K. interpreted results. O.A. and J.M.P.573supplied the replicon and expertise with the Sindbis replicon574system. T.K. supplied source DNA constructs. J.B. and T.E.W.575wrote the manuscript; all authors edited the manuscript.576Notes577The authors declare no competing financial interest.

578■ ACKNOWLEDGMENTS579The authors thank John Scarpa for preparing Figure 1b (using580TinkerCell software, found at http://www.tinkercell.com/581Home/cite) and Andrey Krivoy for input into discussions.582The work presented in this manuscript was supported by583DARPA under grant W911NF-11-054.

584■ ABBREVIATIONS585MEFL,molecules of equivalent fluorescein; EBFP2,enhanced586blue fluorescent protein

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